Related papers: A local-global principle for unipotent characters

This is a survey focusing on the Hasse principle for divisibility of points in commutative algebraic groups and its relation with the Hasse principle for divisibility of elements of the Tate-Shavarevich group in the Weil-Ch\^{a}telet group.…

We study the character theory of inductive limits of $q$-deformed classical compact groups. In particular, we clarify the relationship between the representation theory of Drinfeld-Jimbo quantized universal enveloping algebras and our…

Let $G$ be a unimodular locally compact group. We define a property of irreducible unitary $G$-representations $V$ which we call c-temperedness, and which for the trivial $V$ boils down to F{\o}lner's condition (equivalent to the trivial…

Let D be a connected component of a reductive group over an algebraically closed field. We define a surjective map from the unipotent character sheaves on D to the set of strata of D, extending an earlier result which applied to connected…

We prove Clifford theoretic results on the representations of finite groups which only hold in characteristic $2$. Let $G$ be a finite group, let $N$ be a normal subgroup of $G$ and let $\varphi$ be an irreducible $2$-Brauer character of…

By generalizing Frobenius' polynomial method to good partition algebra, we will develop new character theories for a finite group $G$. A uniform defining equations are derived for these kinds of character theories. The new character…

Publications on automorphic representations of the group U(3) assumed the validity of multiplicity one theorem since I claimed it in 1982. But the argument, published 1988, was based on a misinterpretation of a claim of Gelbart and…

In this note we give applications of recent results coming mostly from the third paper of this series. It is shown that the number of irreducible characters in a $p$-block of a finite group with abelian defect group $D$ is bounded by $|D|$…

The main purpose of this note is to establish an effective version of the Grunwald--Wang Theorem, which asserts that given a family of local characters $\chi^{v}$ of $K_{v}^{*}$ of exponent $m$ where $v \in S$ for a finite set $S$ of primes…

Using Harish-Chandra induction and restriction, we construct a categorical action of a Kac-Moody algebra on the category of unipotent representations of finite unitary groups in non-defining characteristic. We show that the decategorified…

We extend existing results characterizing Weil-Ch\^atelet divisibility of locally trivial torsors over number fields to global fields of positive characteristic. Building on work of Gonz\'alez-Avil\'es and Tan, we characterize when…

Dade's conjecture predicts that if p is a prime, then the number of irreducible characters of a finite group of a given p-defect is determined by local subgroups. In this paper we replace $p$ by a set of primes pi and prove a pi-version of…

We review the categorical representation of a Kac-Moody algebra on unipotent representations of finite unitary groups in non-defining characteristic given by the authors. Then, we extend this construction to finite reductive groups of types…

Let F be a non-archimedean local field and G be the group GL(N,F). Let \pi be a smooth complex representation of G lying in the Bernstein block B(\pi) of some simple type in the sense of Bushnell and Kutzko. Refining the approach of the…

Many of the conjectures of current interest in the representation theory of finite groups in characteristic $p$ are local-to-global statements, in that they predict consequences for the representations of a finite group $G$ given data about…

Let G be the group GL(N,F), where F is a non-archimedean locally compact field. Using Bushnell and Kutzko's simple types, as well as an original idea of Henniart's, we construct explicit pseudo-coefficients for the discrete series…

We prove that Sp\"ath's Character Triple Conjecture holds for every finite group with respect to maximal defect characters at the prime 2. This is done by reducing the maximal defect case of the conjecture to the so-called inductive…

In a recent paper, Colliot-Th\'el\`ene, Parimala and Suresh conjectured that a local-global principle holds for projective homogeneous spaces of connected linear algebraic groups over function fields of p-adic curves. In this paper, we show…

Harish-Chandra classified discrete series representations of real semisimple Lie groups by describing their characters as tempered distributions with an explicit formula on the elliptic set. His approach was inspired by Weyl's proof of the…

We give a cohomological treatment of a character theory for (g,K)-modules. This leads to a nice formalism extending to large categories of not necessarily admissible (g,K)-modules. Due to results of Hecht, Schmid and Vogan the classical…